Question: Solve for $x$ and $y$ using elimination. ${-6x-6y = -60}$ ${5x-5y = -30}$
We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Multiply the top equation by $5$ and the bottom equation by $6$ ${-30x-30y = -300}$ $30x-30y = -180$ Add the top and bottom equations together. $-60y = -480$ $\dfrac{-60y}{{-60}} = \dfrac{-480}{{-60}}$ ${y = 8}$ Now that you know ${y = 8}$ , plug it back into $\thinspace {-6x-6y = -60}\thinspace$ to find $x$ ${-6x - 6}{(8)}{= -60}$ $-6x-48 = -60$ $-6x-48{+48} = -60{+48}$ $-6x = -12$ $\dfrac{-6x}{{-6}} = \dfrac{-12}{{-6}}$ ${x = 2}$ You can also plug ${y = 8}$ into $\thinspace {5x-5y = -30}\thinspace$ and get the same answer for $x$ : ${5x - 5}{(8)}{= -30}$ ${x = 2}$